3 problems

Boundary converse conjecture. If a positive matrix $M \in \mathcal{M}_{\binom{k+1}{2},k}^{p \times q}$ does not have a size-$k$ psd factorization in which all factors have rank $k$…

Rigidity-equivalence conjecture. The conditions b), c), and d) are equivalent for every matrix $M \in \mathcal{M}_{3,2}^{p \times q}$.

The 1-trivial-motion conjecture. The set of $1$-trivial motions of size-$k$ psd factorizations of matrices in $\mathcal{M}_{\binom{k+1}{2},k}^{p \times q}$ is equal to…